A conventionally known vibration-damping device, such as, for example, that shown in Patent Document 1 (Paragraph Nos. [0020] to [0037] and FIGS. 1 to 8), includes a supporting member (bracket member) connected to one of a vibration-generator and a vibration-receiver, and a vibration-damping rubber (vibration-damping member) held in the supporting member. The vibration-damping rubber includes an outer cylinder (first mounting member) fitted inside a fitting hole (fitting part) provided in the supporting member, an inner cylinder (second mounting member) disposed inside the outer cylinder and connected to the other of the vibration-generator and the vibration-receiver, and a rubber part (elastic body) that connects the outer and inner cylinders.
The fitting hole and the outer cylinder are each formed in a true-circular shape in a plan view, and the outer cylinder is pressed inside the fitting hole.
Another conventionally known vibration-damping device, such as, for example, that shown in Patent Document 2, is a sandwich-type vibration-damping device including a pair of vibration-damping members disposed such that the end parts of the outer cylinders (first mounting members) in the axial direction face each other, and plate members (sandwiching members) that sandwich the pair of vibration-damping members from both sides in the axial direction. In this vibration-damping device, the outer cylinders of the pair of vibration-damping members are formed in cylindrical shapes, and are fitted inside a mounting hole (fitting part) that is formed in the bracket member and is circular in a plan view, from both sides thereof in the axial direction. Flange parts are formed at the ends of the outer cylinders on the axial direction outer sides (sides of both sandwiching members), and protrude radially outward. These flange parts sandwich the bracket member.